{
 "title": "Dissipative 5PM-2SF integral families: definitions and sector-label convention",
 "sector_label_convention": "a sector label is the integer sum of 2^i over the propagators i (0-based position in the \"propagators\" list) that appear with positive power; e.g. PX2 sector 1077759 = slots [0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 20]",
 "i0_note": "the i0 routings of the uncut linearized propagators are not part of a family definition: the integration-by-parts system and the flow equations hold for every routing, and the routing enters only through the boundary constants",
 "dimension_and_kinematics": "u1^2 = u2^2 = 1, q^2 = -1, u1.u2 = y (= gamma), u_i.q = 0; the PX2 systems of Sec. 5 sit at y = 5/4",
 "families": {
  "P": {
   "name_in_ref_Driesse_2026": "P",
   "loop_momenta": [
    "k1",
    "k2",
    "k3",
    "k4"
   ],
   "external_vectors": [
    "u1",
    "u2",
    "q"
   ],
   "kinematic_replacements": {
    "u1^2": "1",
    "u2^2": "1",
    "q^2": "-1",
    "u1*u2": "y",
    "u1*q": "0",
    "u2*q": "0"
   },
   "propagators": [
    "2*k1*u1",
    "2*k2*u1",
    "2*k3*u2",
    "2*k4*u2",
    "2*k1*u2",
    "2*k2*u2",
    "2*k3*u1",
    "2*k4*u1",
    "(k1-k2)^2",
    "(k1-k3)^2",
    "(k1-k4)^2",
    "(k2-k3)^2",
    "(k2-k4)^2",
    "(k3-k4)^2",
    "(k1+q)^2",
    "(k2+q)^2",
    "(k3+q)^2",
    "(k4+q)^2",
    "k1^2",
    "k2^2",
    "k3^2",
    "k4^2"
   ],
   "cut": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0
   ],
   "cut_convention": "cut[i]=1: propagator i is a cut worldline delta function delta(2 k.u); cut[i]=0: ordinary denominator (linearized worldline 2k.u or quadratic graviton)",
   "top_level_sectors": [
    306431,
    307967,
    335103,
    340479,
    343391,
    375967,
    376095,
    400127,
    403967,
    408479,
    440927,
    441119,
    552191,
    553727,
    595711,
    599551,
    604015,
    620207,
    620335,
    659199,
    664575,
    667567,
    683631,
    683823,
    1072383,
    1077759,
    1080671,
    1087231,
    1091071,
    1095535,
    1183231,
    1184767,
    1357487,
    1357615,
    1488655,
    1489679,
    1604767,
    1604895,
    1732367,
    1735951,
    2120447,
    2124287,
    2128799,
    2133759,
    2139135,
    2142127,
    2166271,
    2167807,
    2403951,
    2404143,
    2469647,
    2473231,
    2652767,
    2652959,
    2717455,
    2718479
   ],
   "top_level_sectors_as_propagator_slots": {
    "306431": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     13,
     15,
     18
    ],
    "307967": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     12,
     13,
     15,
     18
    ],
    "335103": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     12,
     16,
     18
    ],
    "340479": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     12,
     13,
     16,
     18
    ],
    "343391": [
     0,
     1,
     2,
     3,
     4,
     6,
     8,
     10,
     11,
     12,
     13,
     16,
     18
    ],
    "375967": [
     0,
     1,
     2,
     3,
     4,
     7,
     10,
     11,
     12,
     13,
     15,
     16,
     18
    ],
    "376095": [
     0,
     1,
     2,
     3,
     4,
     8,
     10,
     11,
     12,
     13,
     15,
     16,
     18
    ],
    "400127": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     11,
     12,
     17,
     18
    ],
    "403967": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     11,
     13,
     17,
     18
    ],
    "408479": [
     0,
     1,
     2,
     3,
     4,
     7,
     8,
     9,
     11,
     12,
     13,
     17,
     18
    ],
    "440927": [
     0,
     1,
     2,
     3,
     4,
     6,
     9,
     11,
     12,
     13,
     15,
     17,
     18
    ],
    "441119": [
     0,
     1,
     2,
     3,
     4,
     8,
     9,
     11,
     12,
     13,
     15,
     17,
     18
    ],
    "552191": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     13,
     14,
     19
    ],
    "553727": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     12,
     13,
     14,
     19
    ],
    "595711": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     10,
     12,
     16,
     19
    ],
    "599551": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     10,
     13,
     16,
     19
    ],
    "604015": [
     0,
     1,
     2,
     3,
     5,
     6,
     8,
     9,
     10,
     12,
     13,
     16,
     19
    ],
    "620207": [
     0,
     1,
     2,
     3,
     5,
     7,
     9,
     10,
     12,
     13,
     14,
     16,
     19
    ],
    "620335": [
     0,
     1,
     2,
     3,
     5,
     8,
     9,
     10,
     12,
     13,
     14,
     16,
     19
    ],
    "659199": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     10,
     11,
     17,
     19
    ],
    "664575": [
     0,
     1,
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     8,
     9,
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     19
    ],
    "667567": [
     0,
     1,
     2,
     3,
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     7,
     8,
     9,
     10,
     11,
     13,
     17,
     19
    ],
    "683631": [
     0,
     1,
     2,
     3,
     5,
     6,
     9,
     10,
     11,
     13,
     14,
     17,
     19
    ],
    "683823": [
     0,
     1,
     2,
     3,
     5,
     8,
     9,
     10,
     11,
     13,
     14,
     17,
     19
    ],
    "1072383": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     12,
     14,
     20
    ],
    "1077759": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     12,
     13,
     14,
     20
    ],
    "1080671": [
     0,
     1,
     2,
     3,
     4,
     6,
     8,
     10,
     11,
     12,
     13,
     14,
     20
    ],
    "1087231": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     9,
     10,
     12,
     15,
     20
    ],
    "1091071": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     10,
     13,
     15,
     20
    ],
    "1095535": [
     0,
     1,
     2,
     3,
     5,
     6,
     8,
     9,
     10,
     12,
     13,
     15,
     20
    ],
    "1183231": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     10,
     11,
     17,
     20
    ],
    "1184767": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     9,
     12,
     17,
     20
    ],
    "1357487": [
     0,
     1,
     2,
     3,
     5,
     7,
     9,
     10,
     12,
     13,
     15,
     18,
     20
    ],
    "1357615": [
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     1,
     2,
     3,
     5,
     8,
     9,
     10,
     12,
     13,
     15,
     18,
     20
    ],
    "1488655": [
     0,
     1,
     2,
     3,
     8,
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     12,
     13,
     15,
     17,
     18,
     20
    ],
    "1489679": [
     0,
     1,
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     3,
     8,
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     11,
     12,
     13,
     15,
     17,
     18,
     20
    ],
    "1604767": [
     0,
     1,
     2,
     3,
     4,
     7,
     10,
     11,
     12,
     13,
     14,
     19,
     20
    ],
    "1604895": [
     0,
     1,
     2,
     3,
     4,
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     10,
     11,
     12,
     13,
     14,
     19,
     20
    ],
    "1732367": [
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     2,
     3,
     8,
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     13,
     14,
     17,
     19,
     20
    ],
    "1735951": [
     0,
     1,
     2,
     3,
     8,
     10,
     11,
     12,
     13,
     14,
     17,
     19,
     20
    ],
    "2120447": [
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     2,
     3,
     4,
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     6,
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    ],
    "2124287": [
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     3,
     4,
     5,
     6,
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    ],
    "2128799": [
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    ],
    "2133759": [
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    ],
    "2139135": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
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    ],
    "2142127": [
     0,
     1,
     2,
     3,
     5,
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     8,
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     10,
     11,
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     21
    ],
    "2166271": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     10,
     11,
     16,
     21
    ],
    "2167807": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
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     8,
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    ],
    "2403951": [
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     1,
     2,
     3,
     5,
     6,
     9,
     10,
     11,
     13,
     15,
     18,
     21
    ],
    "2404143": [
     0,
     1,
     2,
     3,
     5,
     8,
     9,
     10,
     11,
     13,
     15,
     18,
     21
    ],
    "2469647": [
     0,
     1,
     2,
     3,
     8,
     9,
     10,
     11,
     13,
     15,
     16,
     18,
     21
    ],
    "2473231": [
     0,
     1,
     2,
     3,
     8,
     10,
     11,
     12,
     13,
     15,
     16,
     18,
     21
    ],
    "2652767": [
     0,
     1,
     2,
     3,
     4,
     6,
     9,
     11,
     12,
     13,
     14,
     19,
     21
    ],
    "2652959": [
     0,
     1,
     2,
     3,
     4,
     8,
     9,
     11,
     12,
     13,
     14,
     19,
     21
    ],
    "2717455": [
     0,
     1,
     2,
     3,
     8,
     9,
     10,
     12,
     13,
     14,
     16,
     19,
     21
    ],
    "2718479": [
     0,
     1,
     2,
     3,
     8,
     9,
     11,
     12,
     13,
     14,
     16,
     19,
     21
    ]
   },
   "source_note": "arXiv:2601.16256 v3 supplement eqs.(16-22) [tex lines 1425-1515]; deltas d(l1.v1) d(l2.v1) d(l3.v2) d(l4.v2); WQFT delta-cut convention (pm4_K3p0 / pm5_2SF_PX2_diss style). P subset {D1,D2,D4,D5} (supplement eq. 18a)",
   "source_file_sha256": "56b954d36641adceac3f51f4916262cca628602fe8044e00939eb0b54d7980ad"
  },
  "PX1": {
   "name_in_ref_Driesse_2026": "NP1",
   "loop_momenta": [
    "k1",
    "k2",
    "k3",
    "k4"
   ],
   "external_vectors": [
    "u1",
    "u2",
    "q"
   ],
   "kinematic_replacements": {
    "u1^2": "1",
    "u2^2": "1",
    "q^2": "-1",
    "u1*u2": "y",
    "u1*q": "0",
    "u2*q": "0"
   },
   "propagators": [
    "2*k1*u1",
    "2*k2*u1",
    "2*k3*u2",
    "2*k4*u2",
    "2*k1*u2",
    "2*k1*u2-2*k2*u2",
    "2*k3*u1",
    "2*k4*u1",
    "(k1-k2)^2",
    "(k1-k3)^2",
    "(k1-k4)^2",
    "(k2-k3)^2",
    "(k2-k4)^2",
    "(k3-k4)^2",
    "(k1+q)^2",
    "(k2+q)^2",
    "(k3+q)^2",
    "(k4+q)^2",
    "k1^2",
    "k2^2",
    "k3^2",
    "k4^2"
   ],
   "cut": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0
   ],
   "cut_convention": "cut[i]=1: propagator i is a cut worldline delta function delta(2 k.u); cut[i]=0: ordinary denominator (linearized worldline 2k.u or quadratic graviton)",
   "top_level_sectors": [
    306431,
    307967,
    335103,
    340479,
    343391,
    375967,
    376095,
    400127,
    403967,
    408479,
    440927,
    441119,
    552191,
    553727,
    595711,
    599551,
    659199,
    664575,
    1072383,
    1077759,
    1080671,
    1087231,
    1091071,
    1183231,
    1184767,
    1488655,
    1489679,
    1604767,
    1604895,
    1732367,
    1735951,
    2120447,
    2124287,
    2128799,
    2133759,
    2139135,
    2166271,
    2167807,
    2469647,
    2473231,
    2652767,
    2652959,
    2717455,
    2718479
   ],
   "top_level_sectors_as_propagator_slots": {
    "306431": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     13,
     15,
     18
    ],
    "307967": [
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     1,
     2,
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     4,
     5,
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     9,
     12,
     13,
     15,
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    ],
    "335103": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     10,
     11,
     12,
     16,
     18
    ],
    "340479": [
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    ],
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    ],
    "376095": [
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    ],
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    ],
    "403967": [
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    ],
    "408479": [
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    ],
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    ],
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    ],
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   "source_note": "arXiv:2601.16256 v3 supplement eqs.(16-22) [tex lines 1425-1515]; deltas d(l1.v1) d(l2.v1) d(l3.v2) d(l4.v2); WQFT delta-cut convention (pm4_K3p0 / pm5_2SF_PX2_diss style). PX1 subset {D1,D3,D4,D5} (supplement eq. 18b)",
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    "u1*q": "0",
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   },
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   "cut_convention": "cut[i]=1: propagator i is a cut worldline delta function delta(2 k.u); cut[i]=0: ordinary denominator (linearized worldline 2k.u or quadratic graviton)",
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   "source_note": "arXiv:2601.16256 v3 supplement eqs.(16-20) [tex lines 1425-1478]: PX2 = {D1,D3,D4,D6}; deltas d(l1.v1) d(l2.v1) d(l3.v2) d(l4.v2); bulk D_ij,(l_i+q)^2,l_i^2. WQFT delta-cut convention (pm4_K3p0 style).",
   "source_file_sha256": "b101ac8e319bb7252a113b7e4284c67a90e78b1d98c5ed54d70f31981de6dcbe",
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   "top_level_sectors_extended_note": "the four first-stage top sectors plus the completion of the top-sector set under the embeddings that realize the K3 and Calabi-Yau sectors (Table 2 \"4 (+36)\"); source px2_top_extension.json sha256 7b74aba46ee62dc63721012f8ba9bc066e266551e48f36d757f6fa173501aa52"
  },
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   "kinematic_replacements": {
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   },
   "propagators": [
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    "2*k2*u1",
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    "2*k1*u2",
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    "2*k3*u1",
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    "(k3-k4)^2",
    "k1^2",
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   "cut_convention": "cut[i]=1: propagator i is a cut worldline delta function delta(2 k.u); cut[i]=0: ordinary denominator (linearized worldline 2k.u or quadratic graviton)",
   "top_level_sectors": [
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   "source_note": "arXiv:2601.16256 v3 supplement eqs.(16-22) [tex lines 1425-1515]; deltas d(l1.v1) d(l2.v1) d(l3.v2) d(l4.v2); WQFT delta-cut convention (pm4_K3p0 / pm5_2SF_PX2_diss style). NP worldline {NP1..NP4} + bulk NP5-15 + dots NP16-18 (supplement eqs. 21-22); dots = ISP slots, top sectors not populated (line 1515)",
   "source_file_sha256": "2f3a565e7575ecab5e58db8787dbcd46d35cd70bcd9e817d5f44a37736a2617c"
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 },
 "PRODUCER": {
  "stamp": "2026-09-11T13:46:46Z",
  "kira_config_sha256": "57fd6c3c5852aa3877cab6ad5c547a9eea8b8ce020d35365a7761e710c5ba0ce",
  "kira_config_note": "sha256 of the Kira integralfamilies.yaml used in the PX2 reductions; kira/integralfamilies.yaml in this package is that file with its comment header rewritten (all non-comment lines byte-identical, checked at packaging)"
 }
}